The purpose of the present project is developing new time-dependent approaches in the electronic correlation and electron-nuclear interaction problems. It is an urgent problem to develop theories which can treat the time-dependent events quantitatively, as well as methods for large-scale systems which are applicable to the molecular design and chemical reaction design. Our focus was, therefore, on the development of new theories and methods and their applications to chemical phenomena : a method for constructing potential energy surfaces, which is crucial for chemical reaction, accurately and efficiently ; a reaction path model based on dynamic reaction path on the potential surfaces ; wave packet method including electron-nuclear interaction ; and the application of these methods to the chemical reactions.A new time-dependent density functional method and an analytic energy gradient method including electron correlation were formulated, and their program code were developed by collaborating Professor Handy. A theory for tunneling in multidimensional potential surfaces was also formulated and applied to polyatomic chemical reactions. An efficient diagonalization method of large Hamiltonian matrices was developed by collaborating Professor Carbo. Numerical tests were performed to verify the accuracy and efficiency of the new algorithm. A wave packet method including electron-nuclear interaction and a method for constructing potential energy surfaces based on the dynamic reaction path were discussed with Professor Cederbaum. The methods mentioned above were applied to the studies of several chemical phenomena such as dissociation mechanisms of polyatomic molecules and fluorescence of radicals.